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研究生：	吳松泉
論文名稱：	植基於橢圓邊界滑動模式之弦波振盪器 Sinusoidal Oscillator Based on Ellipse Boundary Sliding Mode
指導教授：	洪欽銘
學位類別：	碩士 Master
系所名稱：	機電工程學系 Department of Mechatronic Engineering
論文出版年：	2005
畢業學年度：	93
語文別：	中文
論文頁數：	60
中文關鍵詞：	可變結構控制系統、數位弦波振盪器、指數趨近、橢圓邊界滑動模式
英文關鍵詞：	Variable Structure System, Sinusoidal Oscillators, Ellipse Boundary Sliding Mode, Exponential Approach Rule
論文種類：	學術論文
相關次數：	點閱：144 下載：0
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本研究利用可變結構控制理論的滑動模式於數位弦波產生系統的設計，其中系統所產生出來的數位弦波其頻率與振幅均可由可變結構的滑動圓來加以控制，藉著調整滑動圓便可任意產生所需頻率與振幅的數位弦波訊號。
可變結構控制系統的到達模式容易受到系統擾動的影響，由於系統的不確定性、切換元件的延遲等因素，使滑動模式存有不良的顫動現象，於是本研究提出指數趨近的方法提昇到達模式品質。
並設計橢圓邊界區間滑動模式來改善傳統不連續控制的缺點，藉由加入內外的兩個邊界使可變結構控制系統的狀態控制軌跡被限定在這兩邊界區間內切換，使可變結構控制系統大大減少切換的次數，也因此切換元件不致因過度切換而造成疲勞，使整個系統提早損壞，藉由本研究的設計確實能產生穩定的數位弦波。

關鍵詞：可變結構控制系統、數位弦波振盪器、指數趨近、
橢圓邊界滑動模式

Sinusoidal nonlinear oscillators are designed in this dissertation ,in which a sliding ellipse is used instead of the conventional switching hyperplane. Both the desired amplitude and frequency of the sinusoidal oscillator are simply dependent on the equation of sliding ellipse and are independent of plant parameter.
In the traditional variable structure system, hitting time reduction and chattering attenuation are two important but contradictory issues. The thesis employ exponential approach control rule and sector boundary sliding mode to resolve this conflict. A system should be reduced approach time and sensitivity to parameter variance and external disturbance by the exponential approach control rule. The dynamic response of the exponential approach time can be designed by the user himself.
The control rule based on the sector boundary sliding mode can successfully attenuate the chattering phenomena and avoid steady-state of the system error. Finally, we apply this property of this VSS system to design a digital sinusoidal generator system which can generate more stable sinusoidal signal.

Keywords : Variable Structure System, Sinusoidal Oscillators,
Ellipse Boundary Sliding Mode , Exponential Approach Rule

目  錄
中文摘要···························   Ⅱ
英文摘要···························   Ⅲ
目  錄····························   Ⅳ
圖目錄 ···························   Ⅵ
表目錄 ···························   Ⅶ
第一章    緒 論
 1.1研究背景與動機 · ··············   1
1.2 研究目的 ·······················   2
1.3 研究範圍與限制·····················  2
 1.4 研究方法 ·······················   3
 1.5 研究步驟 ·······················   4
 1.6 論文架構 ·······················   5
第二章    文獻探討
   2.1可變結構控制系統理論背景 ················   7
   2.2二階線性可變結構系統 ··················   8
   2.3可變結構系統數學模型與控制律 ·············· 17
2.4可變結構系統到達模式與滑動模式·············  21
2.5數位弦波產生器 ····················  27
   2.6可變結構控制系統滑動模式之弦波振盪器··········  29
第三章    可變弦波振盪器設計
    3.1 可變弦波振盪器架····················  32
3.2 波振盪器滑動模式設計 ·················  33
3.3 指數趨近模式設計 ···················  35
3.4 橢圓邊界滑動模式之弦波振盪器設計············  37

第四章    數位模擬結果與討論
4.1 前言 ·························  42
   4.2 以可變結構產生數位弦波振盪器模·············  43
4.3 橢圓邊界區間滑動模式弦波振盪器模擬  ··········  46
第五章    研究結論與建議
5.1 研究結論  ·······················  57
5.2 後續研究  ·······················  58
參考文獻 ···························  59
作者簡介 ···························  60


圖 目 錄
圖1-1 研究步驟流程圖 ·····················   6
圖2-1 二階線性可變結構系統  ·················  10
圖2-2 不穩定之螺旋結構····················  11
圖2-3 邊際穩定之雙曲線結構··················  11
圖2-4 相位平面劃分······················  12
圖2-5 理想滑動模式······················  12
圖2-6 實際相位平面軌跡圖···················· 13
圖2-7 實際系統時間響應·····················13
圖2-8 修正之相位平面劃分····················14
圖2-9 傳統滑動模式·······················14
圖2-10 滑動模式軌跡圖······················14
圖2-11滑動模式系統時間響應···················14
圖2-12 滑動模式控制圖······················17
圖2-13 α之相位平面劃分·····················19
圖2-14 β之相位平面劃分·····················19
圖2-15 適應性到達模式······················23
圖2-16 滑動到達模式·······················23
圖2-17 理想飽和式控制······················25
圖2-18 滯後飽和式控制······················25
圖2-19 平行滑動層控制······················26
圖2-20 邊界滑動層控·······················26
圖2-21不同頻率弦波振盪器相位平面圖···············28
圖3-1 波振盪可變結構控制器設計架構圖··············32
圖3-2 用滑動圓之弦波振盪器相位平面圖與輸出波形·········35
圖3-3 數趨近模式相位圖·····················35
圖3-4 數趨近控制之相位平面軌跡圖················37
圖3-5 理想與實際滑動模式示意圖·················37
圖3-6 加入內外邊界之橢圓滑動軌跡圖···············41
圖3-7未加入橢圓邊界區間之系統相位軌跡圖············41
圖3-8加入橢圓邊界區間之系統相位軌跡圖·············41
圖4-1系統初始值於滑動圓內之相位軌跡與輸出圖··········44
圖4-2系統初始值於滑動圓外之相位軌跡與輸出圖··········44
圖4-3系統初始值為 之相位軌跡與輸出·········45
圖4-4加入指數趨近法則之相位軌跡圖··············45
圖4-5 系統相位軌跡圖，△A=0.01·················48
圖4-6 系統之弦波輸出波形，△A =0.01···············49
圖4-7系統相位軌跡圖，△A=0.05··················50
圖4-8統之弦波輸出波形，△A =0.05················51
圖4-9系統相位軌跡圖，△A=0.1··················52
圖4-10系統之弦波輸出波形，△A =0.1···············53
圖4-11 加入不同△A橢圓邊界之系統控制u圖 ·········54
圖4-12 傳統可變結構控制模擬··················55

表 目 錄
表2-1 不同的時域響應之系統結···················9
表2-2 可變結構切換控制規····················12
表4-1不同的橢圓邊界對控制切換次數與波形真率關係····55
                                

參考文獻
英文部分
[1] U. Itkis , "Control systems of variable structure " , New York : John Wieley , 1976.
[2] HONG, C. M. and WU, Y. C., " Design of sinusoidal oscillators using variable structure theory. ",International Journal of Electronic, 68, 1005-1010.,1990.
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[5] Fengxi Zhou and D.Grant Fisher, " Continuous sliding mode control " , INT. J. Control , vol. 55 , No. 2, pp. 313-386 , 1993.
[6] Sira-Ramirez, H., "Sliding mode controlled relaxation oscillations. ", IEEE Transactions on Circuits and Systems, 37, 540-543 ,1990.
[7] CHEN, Y. P., and CHENG, M. H., "Design of sinusoidal oscillators using the theory of variable structure system, " International Journal of Electronics, 72, 143-149, 1992.
[8] LIN, J. L., "Sliding mode-controlled sinusoidal oscillators". International Journal of Electronics, 89, 421-428., 2002
[9] Bass, R. M. and Habetler, T. G., "Three-phase sine-wave reference generation using sliding modes". IEEE Power Electronics and Motion Control, vol. 3, 1197 -1201, 1992.
[10] Paschenko, A. and Shapoval, I., "Modified magnetocumulative beamless variable structure oscillator with active antennas. ", IEEE Power Modulator Symposium, 517 -520.,2002.
[11] V. I. Utkin ," Sliding mode in control and Optimization ", Springer Verlag USA , 1992.
[12] V. I. Utkin , " Sliding modes and their applications in variable structure system " ,Moscow : MIR publishers , 1978.
[13] V. I. Utkin , " Sliding mode control design principles and applications to electric drives " ,IEEE Trans. on Indust. Elec. , vol. 40 , No. 1, pp. 23-26 , 1993.
[14] R. A. Decarlo, S. H. Zak , and G. P. Matthews," variable structure control of nonlinear multivariable system：A tutorial ",Proceedings of the IEEE, Vol. 76 , pp. 212-232 , 1988.
[15] John Y. Hung , Weibing Gao and James C. Hung , "Variable structure control of : A survy " , IEEE Trans. on Indust . Elec. ,Vol. 40 , No. 1, pp.2-22 , 1993.
[16] Kohonen T., "An Introduction to Neural Computer ", Neural Networks, Vol. 1 , pp. 3-16 , 1988.
[17] Chiman Kwan; Xu, R.; Wei Liu; Tan, R. ,"Nonlinear control of missile dynamics Decision and Control ", Proceedings of the 37th IEEE Conference, on Vol. 4 , pp. 4685 -4690 , 1998.
[18] Miller, T. W., Glanz, F. H. Kraft & L. G.," Application of a General Learning Algorithm to the Control of Robotic Manipulators", The International Journal of Robotic research,Vol. 6,No.2, pp.84-98, 1987.

中文部分
[19] 陳永平, "可變結構控制設計", 全華 , 民國八十八年九月
[20] 高為炳, "變結構控制理論基礎", 中國科學技術出版社
[21] 郝維華, "雙滑動模式控制" , 碩士論文 , 國立台灣師範大學工業教育研究所,民國八十三年六月
[22] 蘇崇彥, "無顫動積分式可變結構系統之設計", 碩士論文 , 國立台灣師範大學工業教育研究所 , 民國八十三年六月
[23] 羅維恆, "植基於扇形區間滑動模式之小腦模型控制器之研究", 碩士論文 , 國立台灣師範大學工業教育研究所, 民國九十年六月

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